Elastic energy decomposition and limit criteria

• Autorzy: Rychlewski J.
• Języki publikacji: EN

Abstrakty

EN

The well-known yield condition for isotropic materials, known as the M.T. Huber (and R. von Mises, H. Hencky) yield condition, has oryginally been proposed by J.C. Maxwell (see Appendix 2) in 1856. Maxwell and Huber atttributed the following physical sense to the criterion: the material stays elastic as long as the distortion energydoes not reach the critical value. The attempt made by W. Olszak and W. Urbanowski, who tried to generalize the criterion to anisotropic bodies, is not convincing owing to the fact that, in the case of anisotropic media, decomposition of the total elastic energy into the parts connected with the change of volume and the change of shape is impossible. The notion of “energy-ortogonal” states of stress is introduced in the paper. One state of stress is energy-orthogonal to another state of stress if the ?rst one does not perform any work along the deformations produced by the other. The following theorem is proved: each limit criterion may be represented as a certain condition imposed upon a linear combination of elastic energies corresponding to a uniquely determined (for the given material) pari-wise energy-orthogonal, additive components of the total state of stress. Hence, each quadratic criterion has a de?nite energy interpretation. Moreover, it is shown that each limit criterion may be written in the form of an ineguality bounding the accumulated elastic energy. Considered are also the problems of possible forms of coupling of elastic properties of materials with the corresponding limit criteria.

Słowa kluczowe

EN

history; limit; theory of plasticity; elastic decomposition

PL

historia; limit; teoria plastyczności; decomposition; odkształcenie; odkształcenie sprężyste

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2011
• Tom: Vol. 59, iss. 1
• Strony: 31--63
• Opis fizyczny: Bibliogr. 30 poz., rys., wykr.

Twórcy

autor

Rychlewski J.

• Polska Akademia Nauk, Instytut Podstawowych Problemów Techniki, Warszawa

Bibliografia

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